Finite Group Databasebeta

← C2×C4×D5×D7 #11765381

Subgroups — C2×C4×D5×D7 #11765381

Order 1120.

472 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×D7C211yesmaximal, characteristic
2C2×C4×D35C211yesmaximal, characteristic, complemented
3C2×C4×C7×D5C211yesmaximal, characteristic, complemented
4C2×C4×C5×D7C211yesmaximal, characteristic, complemented
5C2×#63304C211yesmaximal, characteristic, complemented
6C2×D5×Dic7C211yesmaximal, characteristic, complemented
7C2×D7×Dic5C211yesmaximal, characteristic, complemented
8C4×D5×D7C218yesmaximal, direct product factor
9C22×D35C2211yescharacteristic
10C22×C7×D5C2211yescharacteristic
11C22×C5×D7C2211yescharacteristic
12C2×D5×D7C418yesdirect product factor
13C2×D5×D7C2214yes—
14C2×C4×C5×C7C2211yescharacteristic, complemented
15C2×Dic35C2211yescharacteristic, complemented
16C4×D35C2214yescomplemented
17C2×C7×Dic5C2211yescharacteristic, complemented
18C4×C7×D5C2214yescomplemented
19C2×C5×Dic7C2211yescharacteristic, complemented
20C4×C5×D7C2214yescomplemented
21#63304C2214yescomplemented
22D5×Dic7C2214yescomplemented
23D7×Dic5C2214yescomplemented
24C22×C4×D7—51nomaximal, Hall
25C22×C4×D5—71nomaximal, Hall
26C22×C5×C7C2311yescharacteristic
27C2×D35C2×C414yescomplemented
28C2×D35C2312yes—
29C2×C7×D5C2×C414yescomplemented
30C2×C7×D5C2312yes—
31C2×C5×D7C2×C414yescomplemented
32C2×C5×D7C2312yes—
33D5×D7C2×C4116yesdirect product factor
34C4×C5×C7C2312yescomplemented
35Dic35C2312yescomplemented
36C5×Dic7C2312yescomplemented
37C7×Dic5C2312yescomplemented
38C23×D7—51no—
39C22×C4×C7—51no—
40C22×Dic7—51no—
41C2×C4×D7—51no—
42C2×C4×D7—51no—
43C2×C4×D7—51no—
44C2×C4×D7—58no—
45C2×C4×D7D511yescharacteristic, direct product factor
46C23×D5—71no—
47C22×C4×C5—71no—
48C22×Dic5—71no—
49C2×C4×D5—71no—
50C2×C4×D5—71no—
51C2×C4×D5—71no—
52C2×C4×D5—78no—
53C2×C4×D5D711yescharacteristic, direct product factor
54C2×C5×C7C22×C412yescomplemented
55C2×C5×C7C2411yescharacteristic
56D35C22×C414yescomplemented
57C5×D7C22×C414yescomplemented
58C7×D5C22×C414yescomplemented
59C23×C7—51no—
60C22×D7—51no—
61C22×D7—58no—
62C22×D7—54no—
63C22×D7C2×D511yescharacteristic
64C2×C4×C7—51no—
65C2×C4×C7—54no—
66C2×C4×C7C2×D511yescharacteristic, complemented
67C2×Dic7—51no—
68C2×Dic7—54no—
69C2×Dic7C2×D511yescharacteristic, complemented
70C4×D7—54no—
71C4×D7—54no—
72C4×D7—54no—
73C4×D7C2×D514yesdirect product factor
74C23×C5—71no—
75C22×D5—71no—
76C22×D5—78no—
77C22×D5—74no—
78C22×D5C2×D711yescharacteristic
79C2×C4×C5—71no—
80C2×C4×C5—74no—
81C2×C4×C5C2×D711yescharacteristic, complemented
82C2×Dic5—71no—
83C2×Dic5—74no—
84C2×Dic5C2×D711yescharacteristic, complemented
85C4×D5—74no—
86C4×D5—74no—
87C4×D5—74no—
88C4×D5C2×D714yesdirect product factor
89C5×C7C23×C411yescharacteristic, complemented, Hall
90C23×C4—351noSylow
91C22×C7—54no—
92C22×C7—52no—
93C22×C7C22×D511yescharacteristic
94C2×D7—54no—
95C2×D7—52no—
96C2×D7—516no—
97C2×D7C4×D514yesdirect product factor
98C2×D7C22×D512yes—
99C4×C7—52no—
100C4×C7C22×D512yescomplemented
101Dic7—52no—
102Dic7C22×D512yescomplemented
103C22×C5—74no—
104C22×C5—72no—
105C22×C5C22×D711yescharacteristic
106C2×D5—74no—
107C2×D5—72no—
108C2×D5—716no—
109C2×D5C4×D714yesdirect product factor
110C2×D5C22×D712yes—
111C4×C5—72no—
112C4×C5C22×D712yescomplemented
113Dic5—72no—
114Dic5C22×D712yescomplemented
115C24—351no—
116C22×C4—51no—
117C22×C4—71no—
118C22×C4—351no—
119C22×C4—358no—
120C22×C4—351no—
121C22×C4—351no—
122C22×C4—351no—
123C2×C7—54no—
124C2×C7C2×C4×D512yescomplemented
125C2×C7C23×D511yescharacteristic
126D7—54no—
127D7C2×C4×D514yesdirect product factor
128C2×C5—74no—
129C2×C5C2×C4×D712yescomplemented
130C2×C5C23×D711yescharacteristic
131D5—74no—
132D5C2×C4×D714yesdirect product factor
133C23—51no—
134C23—71no—
135C23—354no—
136C23—358no—
137C23—351no—
138C2×C4—51no—
139C2×C4—54no—
140C2×C4—71no—
141C2×C4—74no—
142C2×C4—354no—
143C2×C4—354no—
144C2×C4—354no—
145C2×C4—351no—
146C2×C4—354no—
147C2×C4D5×D711yescharacteristic, direct product factor
148C7C22×C4×D511yescharacteristic, complemented, Sylow
149C5C22×C4×D711yescharacteristic, complemented, Sylow
150C22—54no—
151C22—52no—
152C22—74no—
153C22—72no—
154C22—3516no—
155C22—354no—
156C22—352no—
157C22C2×D5×D711yescharacteristic
158C4—52no—
159C4—72no—
160C4—352no—
161C4C2×D5×D712yesdirect product factor
162C2—54no—
163C2—74no—
164C2—354no—
165C2C4×D5×D712yesdirect product factor
166C2C22×D5×D711yescharacteristic
subgroupG/H
center, hypercenterC2×C4D5×D7
commutator, hypocenterC5×C7C23×C4
FrattiniC2C22×D5×D7
FittingC2×C4×C5×C7C22
socleC22×C5×C7C23
prime radicalC22×D5×D7C2
cosocleC2×C5×C7C24
LCSG ▷ C5×C7
UCSC1 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×D35C2semidirect
3. C2×C4×C7×D5C2semidirect
4. C2×C4×C5×D7C2semidirect
5. C2×#63304C2semidirect
6. C2×D5×Dic7C2semidirect
7. C2×D7×Dic5C2semidirect
8. C4×D5×D7C2direct (N × H)
12. C2×D5×D7C4direct (N × H)
14. C2×C4×C5×C7C22semidirect
15. C2×Dic35C22semidirect
16. C4×D35C22semidirect
17. C2×C7×Dic5C22semidirect
18. C4×C7×D5C22semidirect
19. C2×C5×Dic7C22semidirect
20. C4×C5×D7C22semidirect
21. #63304C22semidirect
22. D5×Dic7C22semidirect
23. D7×Dic5C22semidirect
27. C2×D35C2×C4semidirect
29. C2×C7×D5C2×C4semidirect
31. C2×C5×D7C2×C4semidirect
33. D5×D7C2×C4direct (N × H)
34. C4×C5×C7C23semidirect
35. Dic35C23semidirect
36. C5×Dic7C23semidirect
37. C7×Dic5C23semidirect
45. C2×C4×D7D5direct (N × H)
53. C2×C4×D5D7direct (N × H)
54. C2×C5×C7C22×C4semidirect
56. D35C22×C4semidirect
57. C5×D7C22×C4semidirect
58. C7×D5C22×C4semidirect
66. C2×C4×C7C2×D5semidirect
69. C2×Dic7C2×D5semidirect
73. C4×D7C2×D5direct (N × H)
81. C2×C4×C5C2×D7semidirect
84. C2×Dic5C2×D7semidirect
88. C4×D5C2×D7direct (N × H)
89. C5×C7C23×C4semidirect
97. C2×D7C4×D5direct (N × H)
100. C4×C7C22×D5semidirect
102. Dic7C22×D5semidirect
109. C2×D5C4×D7direct (N × H)
112. C4×C5C22×D7semidirect
114. Dic5C22×D7semidirect
124. C2×C7C2×C4×D5semidirect
127. D7C2×C4×D5direct (N × H)
129. C2×C5C2×C4×D7semidirect
132. D5C2×C4×D7direct (N × H)
147. C2×C4D5×D7direct (N × H)
148. C7C22×C4×D5semidirect
149. C5C22×C4×D7semidirect
161. C4C2×D5×D7direct (N × H)
165. C2C4×D5×D7direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D5×D72
C2×C4×D352
C2×C4×C7×D52
C2×C4×C5×D72
C2×#633042
C2×D5×Dic72
C2×D7×Dic52
C4×D5×D72
C22×C4×D75
C22×C4×D57